MinT - Best Known (141−75, 141, s)-Nets in Base 9

Best Known (141−75, 141, s)-Nets in Base 9

(141−75, 141, 165)-Net over F₉ — Constructive and digital

Digital (66, 141, 165)-net over F₉, using

t-expansion [i] based on digital (64, 141, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(141−75, 141, 202)-Net over F₉ — Digital

Digital (66, 141, 202)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−75, 141, 7449)-Net in Base 9 — Upper bound on s

There is no (66, 141, 7450)-net in base 9, because

1 times m-reduction [i] would yield (66, 140, 7450)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 269676 141112 088452 673448 727831 458145 726180 605604 592742 566288 437562 677770 713745 779988 552649 742915 247153 031462 896032 227549 671638 716305 > 9¹⁴⁰ [i]